function sMap = som_lininit(D, varargin)%SOM_LININIT Initialize a Self-Organizing Map linearly.%% sMap = som_lininit(D, [[argID,] value, ...])%%  sMap = som_lininit(D);%  sMap = som_lininit(D,sMap);%  sMap = som_lininit(D,'munits',100,'hexa');% %  Input and output arguments ([]'s are optional): %   D                 The training data.%            (struct) data struct%            (matrix) data matrix, size dlen x dim%   [argID,  (string) Parameters affecting the map topology are given %    value]  (varies) as argument ID - argument value pairs, listed below.%   sMap     (struct) map struct%% Here are the valid argument IDs and corresponding values. The values % which are unambiguous (marked with '*') can be given without the% preceeding argID.%  'munits'       (scalar) number of map units%  'msize'        (vector) map size%  'lattice'     *(string) map lattice: 'hexa' or 'rect'%  'shape'       *(string) map shape: 'sheet', 'cyl' or 'toroid'%  'topol'       *(struct) topology struct%  'som_topol','sTopol'    = 'topol'%  'map'         *(struct) map struct%  'som_map','sMap'        = 'map'%% For more help, try 'type som_lininit' or check out online documentation.% See also SOM_MAP_STRUCT, SOM_RANDINIT, SOM_MAKE.%%%%%%%%%%%%% DETAILED DESCRIPTION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% som_lininit%% PURPOSE%% Initializes a SOM linearly along its greatest eigenvectors.%% SYNTAX%%  sMap = som_lininit(D);%  sMap = som_lininit(D,sMap);%  sMap = som_lininit(D,'munits',100,'hexa');%% DESCRIPTION%% Initializes a SOM linearly. If necessary, a map struct is created% first. The initialization is made by first calculating the eigenvalues% and eigenvectors of the training data. Then, the map is initialized% along the mdim greatest eigenvectors of the training data, where% mdim is the dimension of the map grid.%% REFERENCES%% Kohonen, T., "Self-Organizing Map", 2nd ed., Springer-Verlag, %    Berlin, 1995, pp. 106-107.%% REQUIRED INPUT ARGUMENTS%%  D                 The training data.%           (struct) Data struct. If this is given, its '.comp_names' and %                    '.comp_norm' fields are copied to the map struct.%           (matrix) data matrix, size dlen x dim%  % OPTIONAL INPUT ARGUMENTS %%  argID (string) Argument identifier string (see below).%  value (varies) Value for the argument (see below).%%  The optional arguments can be given as 'argID',value -pairs. If an%  argument is given value multiple times, the last one is used. %%  Here are the valid argument IDs and corresponding values. The values %  which are unambiguous (marked with '*') can be given without the %  preceeding argID.%  'dlen'         (scalar) length of the training data%  'data'         (matrix) the training data%                *(struct) the training data%  'munits'       (scalar) number of map units%  'msize'        (vector) map size%  'lattice'     *(string) map lattice: 'hexa' or 'rect'%  'shape'       *(string) map shape: 'sheet', 'cyl' or 'toroid'%  'topol'       *(struct) topology struct%  'som_topol','sTopol'    = 'topol'%  'map'         *(struct) map struct%  'som_map','sMap'        = 'map'%% OUTPUT ARGUMENTS% %  sMap     (struct) The initialized map struct.%% EXAMPLES%%  sMap = som_lininit(D);%  sMap = som_lininit(D,sMap);%  sMap = som_lininit(D,'msize',[10 10]);%  sMap = som_lininit(D,'munits',100,'rect');%% SEE ALSO% %  som_map_struct   Create a map struct.%  som_randinit     Initialize a map with random values.%  som_make         Initialize and train self-organizing map.% Copyright (c) 1997-2000 by the SOM toolbox programming team.% http://www.cis.hut.fi/projects/somtoolbox/% Version 1.0beta ecco 100997% Version 2.0beta 101199%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% check arguments% dataif isstruct(D),   data_name = D.name;   comp_names = D.comp_names;   comp_norm = D.comp_norm;   D = D.data;  struct_mode = 1; else   data_name = inputname(1);   struct_mode = 0;end[dlen dim] = size(D);% vararginsMap = [];sTopol = som_topol_struct; sTopol.msize = 0; munits = NaN;i=1; while i<=length(varargin),   argok = 1;   if ischar(varargin{i}),     switch varargin{i},      case 'munits',     i=i+1; munits = varargin{i}; sTopol.msize = 0;     case 'msize',      i=i+1; sTopol.msize = varargin{i};                               munits = prod(sTopol.msize);      case 'lattice',    i=i+1; sTopol.lattice = varargin{i};      case 'shape',      i=i+1; sTopol.shape = varargin{i};      case {'som_topol','sTopol','topol'}, i=i+1; sTopol = varargin{i};      case {'som_map','sMap','map'}, i=i+1; sMap = varargin{i}; sTopol = sMap.topol;     case {'hexa','rect'}, sTopol.lattice = varargin{i};      case {'sheet','cyl','toroid'}, sTopol.shape = varargin{i};     otherwise argok=0;     end  elseif isstruct(varargin{i}) & isfield(varargin{i},'type'),     switch varargin{i}.type,      case 'som_topol',      sTopol = varargin{i};      case 'som_map',       sMap = varargin{i};      sTopol = sMap.topol;     otherwise argok=0;     end  else    argok = 0;   end  if ~argok,     disp(['(som_topol_struct) Ignoring invalid argument #' num2str(i)]);   end  i = i+1; endif length(sTopol.msize)==1, sTopol.msize = [sTopol.msize 1]; endif ~isempty(sMap),   [munits dim2] = size(sMap.codebook);  if dim2 ~= dim, error('Map and data must have the same dimension.'); endend%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% create map% map structif ~isempty(sMap),   sMap = som_set(sMap,'topol',sTopol);else    if ~prod(sTopol.msize),     if isnan(munits),       sTopol = som_topol_struct('data',D,sTopol);    else      sTopol = som_topol_struct('data',D,'munits',munits,sTopol);    end  end    sMap = som_map_struct(dim, sTopol); endif struct_mode,   sMap = som_set(sMap,'comp_names',comp_names,'comp_norm',comp_norm);end%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% initialization% train structsTrain = som_train_struct('algorithm','lininit');sTrain = som_set(sTrain,'data_name',data_name);msize = sMap.topol.msize;mdim = length(msize);munits = prod(msize);[dlen dim] = size(D);if dlen<2,    %if dlen==1, sMap.codebook = (sMap.codebook - 0.5)*diag(D); end  error(['Linear map initialization requires at least two NaN-free' ...	 ' samples.']);  return;end% compute principle componentsif dim > 1 & sum(msize > 1) > 1,  % calculate mdim largest eigenvalues and their corresponding  % eigenvectors      % autocorrelation matrix  A = zeros(dim);  me = zeros(1,dim);  for i=1:dim,     me(i) = mean(D(isfinite(D(:,i)),i));     D(:,i) = D(:,i) - me(i);   end    for i=1:dim,     for j=i:dim,       c = D(:,i).*D(:,j); c = c(isfinite(c));      A(i,j) = sum(c)/length(c); A(j,i) = A(i,j);     end  end    % take mdim first eigenvectors with the greatest eigenvalues  [V,S]   = eig(A);  eigval  = diag(S);  [y,ind] = sort(eigval);   eigval  = eigval(flipud(ind));  V       = V(:,flipud(ind));   V       = V(:,1:mdim);  eigval  = eigval(1:mdim);     % normalize eigenvectors to unit length and multiply them by   % corresponding (square-root-of-)eigenvalues  for i=1:mdim, V(:,i) = (V(:,i) / norm(V(:,i))) * sqrt(eigval(i)); end  else  me = zeros(1,dim);  V = zeros(1,dim);  for i=1:dim,     inds = find(~isnan(D(:,i)));    me(i) = mean(D(inds,i),1);    V(i) = std(D(inds,i),1);  end  end% initialize codebook vectorsif dim>1,   sMap.codebook = me(ones(munits,1),:);   Coords = som_unit_coords(msize,'rect','sheet');  cox = Coords(:,1); Coords(:,1) = Coords(:,2); Coords(:,2) = cox;  for i=1:mdim,    ma = max(Coords(:,i)); mi = min(Coords(:,i));     if ma>mi, Coords(:,i) = (Coords(:,i)-mi)/(ma-mi); else Coords(:,i) = 0.5; end  end  Coords = (Coords-0.5)*2;  for n = 1:munits,       for d = 1:mdim,          sMap.codebook(n,:) = sMap.codebook(n,:)+Coords(n,d)*V(:, d)';    end  endelse    sMap.codebook = [0:(munits-1)]'/(munits-1)*(max(D)-min(D))+min(D);end% training structsTrain = som_set(sTrain,'time',datestr(now,0));sMap.trainhist = sTrain;return;%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%